This paper is a study on the invertibility of the commutator of scalar-idempotent elements and scalar-involutory elements of a unitary ring.

本文研究在一有单位元的环中两等元的换位子与两对元的换位子的可逆性问题。

The necessary and sufficient conditions of similarity of two idempotent matrices are proved, the idempotency of linear combinations of two idempotent matrices is discussed.

明了数域上两同阶等阵相似的充条件是它们有相同的秩；给出了等阵的相似标准型；讨论了两等阵的线性组仍是等阵的充条件。